If three moles of an ideal gas at $$300$$ K expand isothermally from $$30 \text{ dm}^3$$ to $$45 \text{ dm}^3$$ against a constant opposing pressure of $$80$$ kPa, then the amount of heat transferred is _________ J.

For an isothermal expansion against a constant opposing pressure:

$$W = -P_{ext} \Delta V$$

$$\Delta V = 45 - 30 = 15 \text{ dm}^3 = 15 \times 10^{-3} \text{ m}^3$$

$$W = -80 \times 10^3 \times 15 \times 10^{-3} = -1200$$ J

For an isothermal process of an ideal gas: $$\Delta U = 0$$.

By the first law: $$q = \Delta U - W = 0 - (-1200) = 1200$$ J.

The amount of heat transferred is $$\boxed{1200}$$ J.